SHOW ALL WORK LOAN PAYMENTS ARE MADE AT THE END OF EACH MONTH When Sarah Jean...

SHOW ALL WORK

LOAN PAYMENTS ARE MADE AT THE END OF EACH MONTH

When Sarah Jean purchased her house 12 years ago, she took out a 30-year mortgage for $220,000. The mortgage has a fixed interest rate of 6 percent compounded monthly.

(a) Compute Sarah Jean’s monthly mortgage payments.

(b) If Sarah Jean wants to pay off her mortgage today, for how much should she write a check? She made her most recent mortgage payment earlier today.

Expert Solution

a.
Formula to calculate monthly payment
Monthly payment	Loan amount/Annuity discount factor

Annuity discount factor	[1-((1+r)^-n)]/r
interest rate is r and number of payments is n

Calculate monthly payment for new car
Monthly interest rate (r )	0.005	6%/12
No of payments (n)	360	30*12

Monthly payment	220000/(1-(1.005^-360))/0.005
Monthly payment	220000/166.7916
Monthly payment	$1,319.01

b.
In this case we will have to calculate present value of monthly payment with 18 years (30 years - 12 years) remaining to pay the loan
Loan amount	Monthly payment*[1-((1+r)^-n)]/r
Loan amount	1319.01*(1-(1.005^-216)/0.005)
Loan amount	1319.01*131.90
Loan amount	$173,974.77

Thus, Sarah will have to pay $173,974.77 if loan is repaid today.

jeff jeffy answered 1 year ago

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